"Making Cross Origin Requests and Using AJAX You must make API requests from your own or an external server where you can store your API credentials securely. Acuity does not support cross origin requests as client side requests expose any authentication that you're using. You can expose specific endpoints on your server for the APIs you'd like to access over AJAX."

I think the option to pursue is using a WebHook using a header to authenticate to their service.

Feel free to contact me off-world iusing the information in my profile if you need assistance with setting this up: